cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A256472 Primes p for which there are exactly as many primes in the range [p^2, p*nextprime(p)] as there are in the range [p*nextprime(p), nextprime(p)^2], where nextprime(p) gives the next prime after prime p.

Original entry on oeis.org

2, 29, 43, 59, 71, 463, 601, 881, 1049, 1103, 1171, 1451, 2311, 2591, 2689, 2693, 2777, 3083, 3089, 3917, 8543, 12889, 13007, 13799, 13873, 13877, 15497, 18457, 19477, 20369, 23017, 25073, 26641, 29179, 32801, 33757, 35327, 41647, 43987, 46279, 47041, 49211, 51577, 63113
Offset: 1

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Author

Antti Karttunen, Mar 30 2015

Keywords

Examples

			For p=2, we have in the range [2*2, 2*3] just one prime {5}, and also in the latter range [2*3, 3*3] just one prime {7}, thus 2 is included in the sequence.
		

Crossrefs

Subsequence of A256484.

Programs

Formula

a(n) = A000040(A256471(n)).

A256474 Numbers n for which there are at least as many primes in the range [prime(n)*prime(n+1), prime(n+1)^2] as in the range [prime(n)^2, prime(n)*prime(n+1)].

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 40, 46, 47, 51, 52, 53, 54, 56, 57, 60, 62, 64, 66, 67, 68, 70, 71, 72, 75, 76, 78, 79, 80, 82, 83, 84, 85, 87, 89, 90, 91, 93, 94, 95, 97, 99, 100
Offset: 1

Views

Author

Antti Karttunen, Mar 30 2015

Keywords

Comments

Positions of nonnegative terms in A256470.

Crossrefs

Complement: A256475.
Union of A256471 and A256476.
Cf. A256484 (corresponding primes).
Cf. A256470.

Programs

A256485 Primes p for which there are more primes in range [p^2, p*nextprime(p)] than in range [p*nextprime(p), nextprime(p)^2], where nextprime(p) gives the next prime after prime p.

Original entry on oeis.org

41, 97, 101, 163, 167, 179, 181, 191, 193, 197, 223, 227, 229, 257, 271, 277, 283, 307, 313, 347, 367, 373, 389, 419, 443, 457, 479, 503, 521, 547, 563, 577, 587, 593, 599, 641, 643, 659, 661, 673, 683, 691, 719, 811, 821, 823, 829, 839, 857, 859, 877, 907, 929, 937, 983, 1009, 1021, 1031, 1051, 1063, 1087, 1091, 1093, 1151, 1153
Offset: 1

Views

Author

Antti Karttunen, Mar 30 2015

Keywords

Examples

			For p=41, we have in range [41*41, 41*43] (1681 .. 1763) 11 primes: {1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759}, while in the latter range [41*43, 43*43] (1763 .. 1849) we have 9 primes: {1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847}, thus 41 is included in the sequence.
		

Crossrefs

Complement among primes: A256484.

Programs

Formula

a(n) = A000040(A256475(n)).
Showing 1-3 of 3 results.